Students deepen their understanding of ratios to investigate proportional relationships, in order to solve multistep, realworld ratio problems using new strategies that rely on proportional reasoning.
Math
Unit 1
7th Grade
In Unit 1, seventh grade students deepen their understanding of ratios to investigate and analyze proportional relationships. They begin the unit by looking at how proportional relationships are represented in tables, equations, and graphs. As they analyze each representation, students continue to internalize what proportionality means, and how concepts like the constant of proportionality are visible in different ways. Students then spend time comparing examples of proportional and nonproportional associations, and studying how all the representations are connected to one another. Finally, in this unit, students will solve multistep, realworld ratio and rate problems using efficient strategies and representations that rely on proportional reasoning (MP.4). These new strategies and representations, such as setting up and solving a proportion, are added to students’ growing list of approaches to solve problems. Throughout the unit, students will engage with MP.2 and MP.6. Translating between equations, graphs, tables, and written explanations requires students to reason both abstractly and quantitatively, and to pay precise attention to units, calculations, and forms of communication throughout their work.
In sixth grade, students were introduced to the concept of ratios and rates. They learned several strategies to represent ratios and to solve problems, including using concrete drawings, double number lines, tables, tape diagrams, and graphs. They defined and found unit rates and applied this to measurement conversion problems. Seventh grade students will draw on these conceptual understandings to fully understand proportional relationships.
Beyond this unit, in Unit 5, seventh grade students will reengage with proportional reasoning, solving percent problems and investigating how proportional reasoning applies to scale drawings. In eighth grade, students connect unit rate to slope, and they compare proportional relationships across different representations. They expand their understanding of nonproportional relationships to study linear functions in the form of $$y=mx+b$$, and compare these to nonlinear functions, such as $$y=6x^2$$.
Pacing: 22 instructional days (18 lessons, 3 flex days, 1 assessment day)
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The following assessments accompany Unit 1.
Have students complete the PreUnit Assessment and PreUnit Student SelfAssessment before starting the unit. Use the PreUnit Assessment Analysis Guide to identify gaps in foundational understanding and map out a plan for learning acceleration throughout the unit.
Have students complete the MidUnit Assessment after lesson 9.
Use the resources below to assess student mastery of the unit content and action plan for future units.
Use student data to drive your planning with an expanded suite of unit assessments to help gauge students’ facility with foundational skills and concepts, as well as their progress with unit content.
Unit Launch
Prepare to teach this unit by immersing yourself in the standards, big ideas, and connections to prior and future content. Unit Launches include a series of short videos, targeted readings, and opportunities for action planning.
Model  Example  
Setting up and solving a proportion 
A group of 4 students buy movie tickets for $24. At this rate, how much would 20 students pay for the movie? $$\frac{4\space \mathrm{students}}{$24} = \frac{20\space \mathrm{students}}{$x}$$ $$4x=24(20)$$ $$x=$120$$ 

Table of equivalent ratios 
The table below shows some weights of rice, in pounds, and their corresponding costs, in dollars.


Equation  The equation $$y=8.75x$$ represents the cost in dollars, $$y$$, to purchase $$x$$ pounds of turkey meat at a deli.  
Graph 
The graph below shows the relationship between the cost of gas and the number of gallons of gas purchased at a gas station. 
commission
constant of proportionality
dependent variable
equivalent ratio
independent variable
part to whole ratio
part to part ratio
proportion
proportional relationship
ratio
rate
unit rate
To see all the vocabulary for Unit 1, view our 7th Grade Vocabulary Glossary.
To see all the materials needed for this course, view our 7th Grade Course Material Overview.
Topic A: Representing Proportional Relationships in Tables, Equations, and Graphs
Topic B: NonProportional Relationships
Topic C: Connecting Everything Together
Topic D: Solving Ratio & Rate Problems with Fractions
Key
Major Cluster
Supporting Cluster
Additional Cluster
CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP4 — Model with mathematics.
CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP6 — Attend to precision.
CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.
CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.
Unit 2
Operations with Rational Numbers